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# Anova

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### Anova

1. 1. Analysis of Variance One-Way Designs; Description of Data, Analysis of Variance, Analysis Using SPSS, ANOVA Assumptions R.A. Fisher Assumptions 1. Population normality 2. Homogeneity of Variance 3. Random Selection 4. More than two populations 5. Independent variables are of nominal scale and Dependent variable is metric, or at least interval scaled.
2. 2. The technique has found applications in the fields of economics, psychology, sociology, business and industry. It becomes handy in situations where we want to compare the means of more than two populations. Some examples could be to compare: • the mean cholesterol content of various diet foods • the average mileage of, say, five automobiles • the average telephone bill of households belonging to four different income groups and so on.
3. 3. Example-1 Suppose we want to compare the cholesterol contents of the four competing diet foods on the basis of the following data (in milligrams per package) which were obtained for three randomly taken samples: Completely Randomized Design in a One-way ANOVA Diet Food A 3.6 4.1 4.0 Diet Food B 3.1 3.2 3.9 Diet Food C 3.2 3.5 3.5 Diet Food D 3.5 3.8 3.8 We want to test whether the difference among the sample means can be attributed to chance at the 5 per cent level of significance.
4. 4. Example-2 The following data refers to the salary package (in Rs. lakhs) offered to MBA graduates with different specializations and having studied at four different business schools. For the sake of simplification, only two students are taken for each interaction between the institute and field of specialization. Factorial Design Specialization Business School I II III IV Marketing 6 4 8 6 5 5 6 4 Finance 7 6 6 9 6 7 7 8 Operation 8 5 10 9 7 5 9 10
5. 5. 1. Analyze 2. Compare Means and One-Way ANOVA… 3. Dependent List: 4. Factors: 5. Options… and One-Way ANOVA:Options 6. Descriptive and Homogeneity of variance test 7. Continue 8. Contrasts… and One-Way ANOVA:Contrasts 9. Coefficients: 10. Add 11. Add 12. Add SPSS Commands of One-Way ANOVA
6. 6. 1. Analyze 2. General Linear Model and Unvariate… 3. Dependent Variable: 4. Fixed Factor(s): 5. Options… 6. Descriptive statistics, Estimates of effect size, Observed Power and Homogeneity tests 7. OK SPSS Commands of Two-Way ANOVA The Levene’s test tells us that the homogeneity of variance assumptions has not been violated. The output illustrates that the main effects for location and store type are not significant (p > .05). Therefore, neither store type nor location significantly influences the sales of toys.